Tension-element drives and especially finely-stranded, stainless-steel cable drives have taken on increased importance in mechanical transmissions used for high-performance automated machines. Increased exploitation of computer control places a higher value on lightweight, compact machines that react quickly to motor commands, and often these characteristics are achieved through the use of tension-element drives. While cable drives are the most common type of tension-element drive used in automated machines, this invention applies also to the broader category of tension-element drives, which extends to tapes/bands, belts, ropes, and chains.
When properly designed, tension-element drives have high material strength, high stiffness, low weight, low velocity ripple, low torque ripple, no backlash, and low friction. Furthermore, they do not leak and do not require surface lubrication. Cables and some other tension-element types can be guided several meters around pulleys through complex and twisting geometries. Cables and all other tension-element drives do not transfer power through compression or shear; and as a result they avoid added compliance and strength limitations found in gear teeth, harmonic drives, linkages, drive shafts, and push rods caused by bending moments or buckling. Cable drives transmit mechanical energy with far greater power density than hydraulic systems because the tensile strength of extruded stainless steel, even derated by a factor of 3 for inter-fiber air gaps, transmits power at an order of magnitude higher stress (400 MPa) compared the highest-pressure hydraulic systems (40 MPa). When designed for reliability, cable drives have a history of dependability in such demanding applications as aerial trams, cable cars, aircraft and missile control surfaces, cranes, and elevators.
High performance in servo-driven cable drives and many other tension-element drives is maintained only when the cables are pretensioned to at least one-half of their maximum operating tensions so that neither of an antagonistic pair of cables becomes slack, even when subjected to full operational motor torque. Pretension is the equal tension present in both cables of a tension-element drive when zero torque is exerted from the drive or driven shafts. With proper pretension TP, the high and low instantaneous tensions TH and TL in a pair of antagonistic cables driven by motor torque τM areTH=TP+τM(rM+rC)>0 andTL=TP−τM(rM+rC)>0,where rC is the cable radius and rM is the wrap radius of the motor shaft. As long as there is adequate pretension in the system before operation, at least some level of tension will remain in both cables under any operating torque, ensuring no slack will form in either cable, even momentarily.
Slack can allow enormous cable loads due to wind-up each time the motor reverses torque. Momentarily the motor is allowed to accelerate in the opposite direction from the rest of the system, increasing its kinetic energy until the slack suddenly disappears and the kinetic energy is instantly converted into very high cable stress causing local yielding in individual cable fibers, and leading to rapid cable stretch and premature cable failure. Pretension prevents this behavior.
Pretensioned cable pairs also exhibit twice the drive stiffness over non-pretensioned cable pairs because both, rather than one, of the cable stiffness contribute in parallel to the overall drive stiffness.
Several methods have been used to apply pretension—e.g. applicant's U.S. Pat. Nos. 5,388,480 and 5,046,375, and applicant's PhD thesis entitled “The Effect of Transmission Design on Force-Controlled Manipulation”, Massachusetts Institute of Technology (1988), the disclosure of which is herein incorporated by reference. The previous pretensioning methods, e.g. those described in Townsend PhD thesis 1988 and U.S. Pat. No. 5,388,480, are not automatic or easily automated. Unfortunately pretensioning is a highly iterative process because local pretension induced in a short segment of the cable drive does not easily migrate to the rest of the drive due to the exponentially nonlinear capstan effect, given by the equation:TH=TL×eμβ,where TH and TL are the tensions at the ends of a cable wrapped β radians around a cylinder with friction coefficient μ between the cylinder and cable surfaces. For stainless-steel cable running on metal or ceramic cylinders, 0.2≦μ≦0.5, and is generally constant in a given design. With μ nearly constant, the exponential capstan equation is extraordinarily sensitive to the number of cable wraps.
For example, assume that the friction coefficient is 0.3, and a cable is wrapped only 5 turns around a pulley. In a hypothetical tug of war, between an ant and an ox pulling on opposite ends of this wrapped cable, the ant would only have to pull with 1 gm (force) to stop an ox pulling with 80 kg (force). The capstan effect guides many design aspects of cable drives. For example, to protect the normally-weaker terminated ends of the cable from high loads, two or three extra wraps of cable beyond the working range of the drive eliminates virtually all shock-load exposure at the terminations. The capstan effect also constrains the design of the popular split-pinion method of enabling pretensioning. In this method the two halves of the motor pinion are allowed briefly during pretensioning, to counter-rotate in the relative direction that eliminates cable slack and induces pretension. This method only works if neither cable straddles the split between the two halves of the motor pinion. If one of the cables straddles the split by more than a wrap or two, capstan effect will prevent relative rotation in the direction required to increase pretension.
A related factor is that cables exhibit higher performance and last longer if the pinion is scalloped with a helix that supports the circular cross-sectional shape of the cable. Otherwise the cable becomes elliptical under the high pressure between the cable and the pinion surface due to the radius of curvature of the wrapped cable. In an active cable drive, the cable repeatedly cycles from elliptical to circular as it wraps and unwraps off the pinion and pulley surfaces. When a pinion drives a larger diameter pulley, this lateral pressure is greater on the pinion by the ratio of their diameters. It is impractical to align the scallop patterns between a pinion and a pulley, partly because the process of pretension will change the alignment over the lifetime of the cable. But since the unwanted pressure is much higher on the pinion, the pinion alone is scalloped. However, pretensioning split in the pinion creates a similar alignment dilemma as the cables are pretensioned over their lifetime. Therefore, in known pretensioning systems, the pinion is only scalloped on one side of the pinion split with the other side left as a simple cylindrical surface that matches the radius of the bottom point of the scallop.
Cable damage due to cycling between circular and elliptical cross-sections depends on the frequency of cycling. A histogram of the most active locations of the average drive approximates a Gaussian distribution with the highest activity near the middle of the drive range and the least activity at each extreme of the drive range. Therefore, known designs place the pinion split near the extreme edge of the drive range so that actively cycling cable is nearly always supported by the scallop. As a result, the ends of the drive range are rarely used.
A cable pretensioner will only impose and store a local pretension in the compliance of the usually-short free span of cable between pulley tangents and just a couple of radians of the wrapped cable nearest the free span. The rest of the 90+% of cable is unaffected. The only way to migrate the pretension into the remainder of the wraps is to run the cable drive back and forth several times across its full range. This back-and-forth motion distributes the local pretension across the entire cable, leaving a weak but nearly uniform global pretension. To bring the pretension up to proper levels across the entire cable drive requires repeating the process multiple times. As a result, cable drives either are never pretensioned by the user or inadequately pretensioned, resulting in increased compliance, backlash, and rapid cable deterioration.
The worst drawback of tension-element drives is the lack of technicians familiar with their unique service requirements. For the strong benefits of tension-element drives to enjoy wider acceptance, users must be freed from the steep cable-maintenance learning curve and its tedious application. Through automatic pretensioning, the most important and tedious maintenance procedure for tension-element drives becomes virtually invisible to the user. Instead of teaching each user how to measure and maintain cable pretension, embedded machine intelligence applies this knowledge directly and with precision.